# Usage of $\leadsto$ compared to other symbols [duplicate]

I noticed that not a lot of authors of math books don't use the $$\leadsto$$ to denote the next step. As far as I understand it, that is supposed to mean "the next step of the proof is". Instead, I notice that they use $$=$$ to mean the same thing, or also $$\implies$$ or $$\iff$$. Which symbol is the most appropriate for stating the next step? Can we use $$\implies$$ and $$\leadsto$$ interchangeably? Is this accepted in formal proofs?

• @kimchilover partially, yes, but it's not clear if we can interchangeably use $\leadsto$ with $\implies$...it seems to suggest that $\leadsto$ can be used, but also $\implies$ provided that it is used with a condition and somewhere else in the proof that the condition exists. I'd still like to know what would be much clearer to a reader who reads proofs – Paco G Mar 5 '20 at 0:03

Don't introduce new notation if you can help it. Yes, it might sometimes be worthwhile to introduce new notation, for a rather complex concept that repeats often enough (e.g. Landau's $$O()$$, later extended by Knuth to $$\Omega()$$, $$\Theta()$$, and so on). "Next step is..." just doesn't cut it.